Question

Inequality for convolution $| f *g| \le \|f\|_1 \|g\|_1$

score 61 · Answer 1 · 2026-04-17 10:56:49

61

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Inequality for convolution $| f *g| \le \|f\|_1 \|g\|_1$

Published on 17 Apr 2026 - 10:56

score 1.4k · Answer 2 · 2026-04-12 10:31:39

1.4k

Views

Proof that for the Lebesgue indefinite integral, $\int_E fd\mu(x)=0$ implies $f=0$ almost everywhere

Published on 12 Apr 2026 - 10:31

score 104 · Answer 3 · 2026-04-12 17:43:35

104

Views

Integral on set sequence is not convergent to their countable intersection

Published on 12 Apr 2026 - 17:43

score 131 · Answer 4 · 2026-04-16 13:41:00

131

Views

Does $\int_0^\infty f(x) dx = \lim_{n \to \infty} \int_0^n f(x) dx$ for $f \geq 0$ or $f$ not positive?

Published on 16 Apr 2026 - 13:41

score 126 · Answer 5 · 2026-04-13 16:10:09

126

Views

Lebesgue's differentiation theorem for all points

Published on 13 Apr 2026 - 16:10

score 102 · Answer 6 · 2026-04-13 21:51:46

102

Views

Riemannian Volume vs. Euclidean Volume

Published on 13 Apr 2026 - 21:51

score 78 · Answer 7 · 2026-04-15 19:00:52

78

Views

$\int_{0}^{\infty} x^{a-1}(e^x-1)^{-1}dx $

Published on 15 Apr 2026 - 19:00

score 27 · Answer 8 · 2026-04-15 16:43:37

27

Views

$g$ is differentiable and $g'(y)=\int_{\mathbb{R}}ixf(x)e^{iyx}dm(x)$

Published on 15 Apr 2026 - 16:43

score 671 · Answer 9 · 2026-04-12 16:52:25

671

Views

Integration on manifolds and improper integration

Published on 12 Apr 2026 - 16:52

score 206 · Answer 10 · 2026-04-14 08:30:57

206

Views

$x^{-1}\sin x$ is not integrable on $[0,\infty)$ implies $e^{-xy}\sin x$ is not integrable on $[0,\infty) \times [0,\infty)$

Published on 14 Apr 2026 - 8:30

score 116 · Answer 11 · 2026-04-14 20:10:50

116

Views

Integral of $\int_{0}^{\infty} e^{-ax}\Sigma_{0}^{\infty} \frac{(-1)^n x^{2n}}{4^n (n!)^2}dx $

Published on 14 Apr 2026 - 20:10

score 184 · Answer 12 · 2026-04-16 06:13:24

184

Views

Integration of $\int_{0}^{1} x^{a}(1-x)^{-1}\log (x) dx $

Published on 16 Apr 2026 - 6:13

score 5.1k · Answer 13 · 2026-04-11 09:24:28

5.1k

Views

A rigorous meaning of "induced measure"?

Published on 11 Apr 2026 - 9:24

score 368 · Answer 14 · 2026-04-11 10:39:46

368

Views

Question about definition of the Lebesgue integral of a non-negative function

Published on 11 Apr 2026 - 10:39

score 211 · Answer 15 · 2026-04-16 05:43:08

211

Views

Use the Lebesgue's Monotone Convergence Theorem and the fact that $\int^\infty_0t^ne^{-t}dt=n! \text{ to prove that }\int^\infty_0f(t)e^{-t}dt=s.$

Published on 16 Apr 2026 - 5:43

List Question

Inequality for convolution $| f *g| \le \|f\|_1 \|g\|_1$

Proof that for the Lebesgue indefinite integral, $\int_E fd\mu(x)=0$ implies $f=0$ almost everywhere

Integral on set sequence is not convergent to their countable intersection

Does $\int_0^\infty f(x) dx = \lim_{n \to \infty} \int_0^n f(x) dx$ for $f \geq 0$ or $f$ not positive?

Lebesgue's differentiation theorem for all points

Riemannian Volume vs. Euclidean Volume

$\int_{0}^{\infty} x^{a-1}(e^x-1)^{-1}dx $

$g$ is differentiable and $g'(y)=\int_{\mathbb{R}}ixf(x)e^{iyx}dm(x)$

Integration on manifolds and improper integration

$x^{-1}\sin x$ is not integrable on $[0,\infty)$ implies $e^{-xy}\sin x$ is not integrable on $[0,\infty) \times [0,\infty)$

Integral of $\int_{0}^{\infty} e^{-ax}\Sigma_{0}^{\infty} \frac{(-1)^n x^{2n}}{4^n (n!)^2}dx $

Integration of $\int_{0}^{1} x^{a}(1-x)^{-1}\log (x) dx $

A rigorous meaning of "induced measure"?

Question about definition of the Lebesgue integral of a non-negative function

Use the Lebesgue's Monotone Convergence Theorem and the fact that $\int^\infty_0t^ne^{-t}dt=n! \text{ to prove that }\int^\infty_0f(t)e^{-t}dt=s.$

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